A Study of the Surviving Fraction of the Cosmic-Ray Radioactive Decay Isotopes 10Be, 26Al, 36Cl and 54Mn as a Function of Energy Using the Charge Ratios Be/B, Al/Mg, Cl/Ar, and Mn/Fe Measured on HEAO3

We have used published HEAO3 data on the charge ratios Be/B, Al/Mg, Cl/Ar, and Mn/Fe to examine the decay of the radioactive cosmic-ray isotopes¹⁰Be, ²⁶Al, ³⁶Cl, and ⁵⁴Mn at energies from ~600 MeV to 20 GeV nucleon^-1. From these charge data we can obtain the surviving fractions of these isotopes at higher energy with a comparable accuracy to that obtained using directly measured low-energy isotopic ratios. As a result of the relativistic time dilation of the lifetimes, these higher energy surviving fractions are a probe of propagation conditions outside the disk and into the halo of the Galaxy. The data are interpreted in terms of a simple leaky-box propagation model, then a more realistic diffusion model, and finally a still more realistic Monte Carlo diffusion model for the propagation of cosmic rays. Interpreted in terms of a leaky-box model, the data for all four isotopes suggest to varying degrees that the cosmic-ray particles are propagating into regions of lower density away from the disk. The diffusion model allows one to determine that the scale size of this extended propagation region in the Z-direction is 2-4 kpc. The data are consistent only with weak Galactic winds ~20 km s^-1 or less. Monte Carlo models require cosmic-ray lifetimes ~20-30 × 10⁶ yr and a halo size 2-3 kpc. The Monte Carlo calculations suggest that it is the scale size of the diffusion coefficient in the Z-direction relative to the halo size that determines the surviving fractions of these radioactive isotopes at high energies rather than the details of the Z dependence of the matter density.